Asymptotic expansions for dervatives of stable laws (Q1176050)

Let \(p^{(k)}(\cdot;\alpha,\gamma)\) be the \(k\)-th derivative of the stable density with index \(\alpha\) and asymmetry parameter \(\gamma\); explicit formulas are know for the associated Fourier transforms. The author applies the saddle point method to the Fourier inversion formula to determine the asymptotic behaviour of \(p^{(k)}(x;\alpha,\gamma)\) as \(k\) tends to infinity and \(x\) varies with \(k\).